this paper, deals with some equivalence relations in fuzzy subgroups. further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

Let A be a finite, nonempty subset of an abelian group. We show that if every element is sum two other elements, then has zero-sum subset. That is, (finite, nonempty) sum-full group not zero-sum-free.

We prove that a non-abelian superstable CSA-group has an infinite definable simple subgroup all of whose proper definable subgroups are abelian. This imply in particular that the existence of non-abelian CSAgroup of finite Morley rank is equivalent to the existence of a simple bad group all whose definable proper subgroups are abelian. We give a new proof of a result of E. Mustafin and B. Poiza...

Determining the order and the structure of the automorphism group of a finite p-group is an important problem in group theory. There have been a number of studies of the automorphism group of p-groups. Most of them deal with the order of Aut(G), the automorphism group of G, see for example [1] and [6]. Moreover various attempts have been made to find a structure for the automorphism group of a ...

We study under what conditions the conjectured one-wayness of the knapsack function (with polynomially bounded inputs) over an arbitrary finite abelian group implies that the output of the function is pseudorandom, i.e., computationally indistinguishable from a uniformly chosen group element. Previous work of Impagliazzo and Naor (J. Cryptology 9(4):199-216, 1996) considers only specific famili...

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig–Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for H without using a relation matrix. The problem of computing a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian group G is addres...